why is my local script not running locally?

local start = game.Workspace:FindFirstChild("Start")
local endPart = game.Workspace:FindFirstChild("End")
local textlabel = script.Parent
local finished = script.Parent.finished

local function timer()
	for t = 0,math.huge,0.05 do
		wait(0.0499999999)
		if finished.Value == true then break end
		local stringT = tostring(t)
		if #(tostring(t)) == 3 then
			t = t.."0" 
		elseif #(tostring(t)) == 1 then
			t = t..".00"
		end
		textlabel.Text = tostring(t)
	end
end

start.Touched:Connect(function(hit)
	if not game.Players:GetPlayerFromCharacter(hit.Parent) then return end
	local player = game.Players:GetPlayerFromCharacter(hit.Parent)
	local character = hit.Parent
	timer()
end)

endPart.Touched:Connect(function(hit)
	finished.Value = true
	wait(0.3)
	finished.Value = false
end)

the code on top is for a timer. the timer starts when the players touches the "start" part and ends when player touches the "end" part

this is in a local script but for some reason the timer runs for every players, meaning globally. im confused, why is this running globally and not locally even though its a local script

local script is in StarterGui>ScreenGui>TextLabel>Localscript

any help is greatly appreciated!

You have to check if the player who touched the part is the localplayer!!!

local start = game.Workspace:FindFirstChild("Start")
local endPart = game.Workspace:FindFirstChild("End")
local textlabel = script.Parent
local finished = script.Parent.finished

local function timer()
    for t = 0,math.huge,0.05 do
        wait(0.0499999999)
        if finished.Value == true then break end
        local stringT = tostring(t)
        if #(tostring(t)) == 3 then
            t = t.."0" 
        elseif #(tostring(t)) == 1 then
            t = t..".00"
        end
        textlabel.Text = tostring(t)
    end
end

start.Touched:Connect(function(hit)
    if not game.Players:GetPlayerFromCharacter(hit.Parent) then return end
    local player = game.Players:GetPlayerFromCharacter(hit.Parent)
if player.Name == game.Players.LocalPlayer.Name then -- check if playername is localplayer
    local character = hit.Parent
    timer()
end -- end
end)

endPart.Touched:Connect(function(hit)
    local player = game.Players:GetPlayerFromCharacter(hit.Parent)
if player.Name == game.Players.LocalPlayer.Name then -- check if playername is localplayer
    finished.Value = true
    wait(0.3)
    finished.Value = false
end -- end
end)